I'm not aware of any study of the Meiji era which attributes the pace of Japan's modernization to the rangaku scholars' scientific knowledge.

The rapidity of Japan's modernization was driven by the Meiji government, primarily composed of leaders from the domains which overthrew the Tokugawa shogunate. Rangaku scholars were closely identified with the shogunate, and therefore tended to be marginalized from leading government roles. While they may have agreed with the rapid modernization (and they largely did), they were not responsible for it.

As for the importance of their scientific knowledge, this simply didn't play as significant a role as is often imagined. In contrast to the shogunate's attempt to carefully control who was allowed to learn about such things, in the Meiji era the doors were thrown open. Western scientists and scholars flooded in, while Japanese students went abroad to learn. The idea that Western learning was something specialized by an elite group was quickly swamped in a general rush for education about such things.

But that's not to say that rangaku scholars were silent or without influence. One of the most influential figures of the era (despite never holding an official government position) was a former Rangaku scholar named Fukuzawa Yukichi. He was at varying times an author, teacher, journalist, and founder of a university. But his importance to the Meiji reforms was more akin to a public intellectual. Fukuzawa seemingly thought about everything that had to do with reforming the nation on a Western model, and published his ideas continually to a nation-wide readership. While he was never in an official role to decide which reforms to take, those who were in such roles were profoundly influenced by his ideas.

Remember, at the time the West (which was certainly the model Japan wanted to emulate) was hardly a single unified entity. Western nations varied incredibly in the forms of their government, industry, economics, education, military, and many other things. Yet somehow they all ended up in the treasured category Fukuzawa called "civilized." How could Japan emulate their example when there were so many seemingly contradictory examples out there? And how could they do this while preserving the concept of Japan as a distinct nation with its own unique identity? What had to change, what should be the model of the change, and what could be preserved? These were all very open questions, and being asked about almost every aspect of society at once.

Fukuzawa's role is illustrative of the kind of influence rangaku scholars had upon the Meiji reforms. It wasn't the depth of their knowledge of Western science that had an impact upon the modernization. Rather it was their ability to conceptualize what aspects of Japan had to change in order to reinvent itself along a Western model. It was as much their understanding of Japan as their understanding of the West which allowed them to contribute meaningfully to reform (Nishi Amane is another prominent example of this).

Recommended sources:

The Autobiography of Fukuzawa Yukichi is highly recommended, as a first hand account from the most famous and influential rangaku scholar of them all.

I'd also recommend Marius Jansen's The Making of Modern Japan for a more comprehensive overview of the period. (Note: Jansen doesn't call out rangaku scholars as a group, but does record the important contributions of key individuals like Fukuzawa and Nishi).